Competitive Langmuir adsorption isotherm

Figure 4.6 shows the competitive adsorption of mephobarbital by activated carbon in the presence of phenobarbital. It clearly illustrates that the extent of mephobarbital adsorption decreases in the presence of phenobarbital. This result shows that the two solutes are competing for the same adsorption sites on the activated carbon. The extent of mephobarbital adsorption in the presence of phenobarbital can be predicted by the competitive Langmuir adsorption isotherm. 

Competitive Langmuir Adsorption Isotherm When two or more substances can be adsorbed on a surface, the so-called competitive isotherms are applied. The Langmuir isotherm was improved for the adsorption of two gases by Markham and Benton (1931). Of course, the four assumptions of Langmuir isotherms are valid here, too. The surface-adsorbed quantity of component 1 is... 

The values for the concentration or occupancy 0 must be determined from the competitive Langmuir adsorption isotherm ... 

The form of the competitive Langmuir adsorption isotherm will not be derived here, but it has been derived by Adamson (1976) for two competing gases on a surface. 

The multicomponent Langmuir adsorption isotherm given in Eq. (7) is the simplest model for the description of non-linear, multicomponent, adsorption equilibrium. At high concentration, the model predicts saturation of the stationary phase and overload of the chromatographic column. At low concentration (high dilution) the behavior can be correctly described by the non-competitive linear adsorption isotherm ... 

A number of classic rate expressions are commonly used to characterize heterogeneous reactions. These include expressions for the Langmuir adsorption isotherm, competitive... 

From the discussion of the Langmuir adsorption isotherm above, it is easy to write the analogous reaction-rate expressions for such competitive adsorption ... 

Theory of Vapor-Particle Partitioning of PAH Compounds in the Atmosphere. Yamasaki et al. (64) treated semivolatile PAHs as inherently vapor-phase materials, existing in the particle phase only because of their tendency to sorb on nonvolatile materials. Under this assumption, the proportion in each phase should vary with the available surface area for sorption and with the ambient temperature. They assumed that sorption followed a Langmuir adsorption isotherm, requiring that there be only a low fractional coverage of the particulate matter with semivolatile material. In this case, competition for sorption sites can be ignored. At equilibrium, the rate of sorption equals the rate of evaporation. They derived this relationship ... 

This equation can be interpreted in terms of Langmuir adsorption isotherms. It is assumed (see 1.5.4) that both reactants must be adsorbed in order to react and that KA and KB are the respective Langmuir adsorption equilibrium constants. The denominator allows for competition for sites between... 

Mg2+ influences calcite dissolution rates the same way, but not to the same extent as Ca2+. The inhibition effects of Mg2+ can be described in terms of a Langmuir adsorption isotherm. Sjoberg (1978) found he could model results for the combined influences of Ca2+ and Mg2+ in terms of site competition consistent with ion exchange equilibrium. The inhibition effects of Mg2+ in calcite powder runs increase with increasing Mg2+ concentration and as equilibrium is approached. 

This effect is relatively small until the total magnesium ion concentrations reach about 1000 ppm. o The effect of Mg2+ concentration on limestone dissolution rate can be explained by a surface adsorption model. The adsorption of Mg2+ reduces the limestone dissolution rate because the surface is partially blinded by the adsorbed magnesium ions. The competitive adsorption of calcium and magnesium ions was described by a mathematical model based on the Langmuir adsorption isotherm. The model was used to explain the sensitivity of limestone dissolution rate to magnesium ion concentration under limestone DA operating conditions. 

Binary mixtures of 1,3,5-tri-tert-butyl-benzene (TTB) and 1,3,5-tri-hydroxyben-zene (PFIL) were used as the feed. The separation was carried out on a 0.46 x 25 cm coluiim packed with microcrystaUine cellulose triacetate, with an average particle size of 5 im. Two different volumes (10 and 50 jiL) of mixtures of different compositions (1 1, 1 3, and 3 1) were injected into the column. All the experiments were performed imder isocratic conditions, with pure methanol as the mobile phase, and low concentration samples. Teoh et al. [65] ignored the competitive adsorption between the two feed components on the grounds that their colimm was efficient, the band resolution rather high, and the samples used rather dilute. So, they assumed that each compoimd follows single-component Langmuir adsorption isotherm behavior, with... 

For describing the kinetics of heterogenous catalytic reactions, the Langmuir adsorption isotherms are used mainly. We now derive them for associative, dissociative, and competitive adsorption. The main assumptions are the following ... 

Hoeft [44] also studied the cooperative and competitive adsorption of ionic surfactant mixtures onto hydrophobic surfaces. When shorter alkyl chain surfactants (sodium octyl sulfonate and sodium decyl sulfonate) are adsorbed, the decyl will displace the octyl surfactant. For mixtures of sodium dodecyi sulfonate and sodium octyl sulfonate, however, there appears to be an association between the surfactant molecules leading to enhanced adsorption of the sodium dodecyi sulfonate with no depletion of the octyl sulfonate adsorption. This is shown in Fig, 2, where the lines indicate the expected adsorption determined using a two-component Langmuir adsorption isotherm with the adsorption parameters determined analyzing the data from adsorption of each species individually. Also shown in Fig. 2 is the concentration of surface-active materials in the aqueous phase at equilibrium. In each of these experiments the total molar concentration and amount of surfactant solution added to the latex was a constant, as was the amount of latex. Thus a lower value for the bulk concentration corresponds to greater adsorption. 

Nonlinearity of the Langmuir adsorption isotherms is observed even in non-competitive chromatographic processes. Individual adsorption isotherms can be found experimentally using frontal analysis at overload conditions however, the adsorption isotherms in the separation of mixtures are different because of the interference with other compounds. In PHPLC method development efforts to optimize preparative chromatography using software... 

Table 2.1 lists the Langmuir adsorption isotherms for several important cases, including dissociative adsorption of a diatomic molecule, and competitive adsorption of two molecules. Note that the fraction of unoccupied sites, 0, equals 1 over the denominator of the Langmuir expression. Isotherms can always be written in the form 9 = Kji A 9, which will appear very useful in solving the rate equations of complex catalytic mechanisms. 

The separate adsorption isotherms for gases A and B on a certain solid obey the Langmuir equation, and it may be assumed that the mixed or competitive adsorption obeys the corresponding form of the equation. 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

The knowledge of these adsorption isotherms allows quantification of the respective affinity for the stationary phase with respect to the different solutes. Many different isotherm equations have been described in the literature, and experimental methods allowing their determination are reviewed by [58]. As a first approximation, modified competitive Langmuir isotherms can often he used ... 

Electrolytes are used to promote the exhaustion of direct or reactive dyes on cellulosic fibres they may also be similarly used with vat or sulphur dyes in their leuco forms. In the case of anionic dyes on wool or nylon, however, their role is different as they are used to facilitate levelling rather than exhaustion. In these cases, addition of electrolyte decreases dye uptake due to the competitive absorption of inorganic anions by the fibre and a decrease in ionic attraction between dye and fibre. In most discussions of the effect of electrolyte on dye sorption, attention is given only to the ionic aspects of interaction. In most cases, this does not create a problem and so most adsorption isotherms of water-soluble dyes are interpreted on the basis of Langmuir or Donnan ionic interactions only. There are, however, some observed cases of apparently anomalous behaviour of dyes with respect to electrolytes that cannot be explained by ionic interactions alone. 

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